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Learning To Help: Training Models to Assist Legacy Devices

Yu Wu, Anand Sarwate

TL;DR

This work addresses extending ML inference to legacy devices by offloading to edge servers through a Learning to Help framework, where a fixed local classifier $m(x)$ is assisted by a learnable edge classifier $e(x)$ and a rejection rule $r(x)$. By formulating a generalized 0-1 loss with abstention cost $c_e$ and edge error cost $c_1$, the authors derive Bayes-optimal rules, establish a generalization bound via Radamacher complexity, and introduce a convex, differentiable surrogate loss $L_S$ with calibration guarantees to train the edge and rejector. Empirical results on CIFAR-10 binary tasks show that Learning to Help outperforms confidence-based rejection methods and benefits from joint training of $r$ and $e$ while keeping $m$ fixed. The framework offers a practical pathway to prolong legacy hardware functionality in MEC settings and motivates future work on multi-server extensions and broader deployment scenarios.

Abstract

Machine learning models implemented in hardware on physical devices may be deployed for a long time. The computational abilities of the device may be limited and become outdated with respect to newer improvements. Because of the size of ML models, offloading some computation (e.g. to an edge cloud) can help such legacy devices. We cast this problem in the framework of learning with abstention (LWA) in which the expert (edge) must be trained to assist the client (device). Prior work on LWA trains the client assuming the edge is either an oracle or a human expert. In this work, we formalize the reverse problem of training the expert for a fixed (legacy) client. As in LWA, the client uses a rejection rule to decide when to offload inference to the expert (at a cost). We find the Bayes-optimal rule, prove a generalization bound, and find a consistent surrogate loss function. Empirical results show that our framework outperforms confidence-based rejection rules.

Learning To Help: Training Models to Assist Legacy Devices

TL;DR

This work addresses extending ML inference to legacy devices by offloading to edge servers through a Learning to Help framework, where a fixed local classifier is assisted by a learnable edge classifier and a rejection rule . By formulating a generalized 0-1 loss with abstention cost and edge error cost , the authors derive Bayes-optimal rules, establish a generalization bound via Radamacher complexity, and introduce a convex, differentiable surrogate loss with calibration guarantees to train the edge and rejector. Empirical results on CIFAR-10 binary tasks show that Learning to Help outperforms confidence-based rejection methods and benefits from joint training of and while keeping fixed. The framework offers a practical pathway to prolong legacy hardware functionality in MEC settings and motivates future work on multi-server extensions and broader deployment scenarios.

Abstract

Machine learning models implemented in hardware on physical devices may be deployed for a long time. The computational abilities of the device may be limited and become outdated with respect to newer improvements. Because of the size of ML models, offloading some computation (e.g. to an edge cloud) can help such legacy devices. We cast this problem in the framework of learning with abstention (LWA) in which the expert (edge) must be trained to assist the client (device). Prior work on LWA trains the client assuming the edge is either an oracle or a human expert. In this work, we formalize the reverse problem of training the expert for a fixed (legacy) client. As in LWA, the client uses a rejection rule to decide when to offload inference to the expert (at a cost). We find the Bayes-optimal rule, prove a generalization bound, and find a consistent surrogate loss function. Empirical results show that our framework outperforms confidence-based rejection rules.
Paper Structure (24 sections, 3 theorems, 38 equations, 4 figures, 1 table, 3 algorithms)

This paper contains 24 sections, 3 theorems, 38 equations, 4 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Related Work
  4. Learning to Reject
  5. Learning to Defer
  6. Learning to Help for a legacy client
  7. Bayes-optimal decision rules
  8. Generalization Bound
  9. Surrogate Loss
  10. Experiments
  11. Conclusion
  12. Key assumptions for learning to help framework
  13. Proof for Equation of $P(M\neq Y \mid X=x)$
  14. Proof for Bayes-optimal decision rules
  15. Proof for Rademacher Upper bound
  16. ...and 9 more sections

Key Result

Theorem 1

Let $\mathcal{R}$ and $\mathcal{E}$ be families of functions that are mapping to $\{-1, +1\}$. Let $e(x)$ be a fixed function that only takes value in $\{-1, +1\}$. We let $R$ denote expected loss of (c1celLoss) and $\hat{R}$ denote the empirical expected loss, $n$ is the sample size, $c_{e}$ denote where $\Hat{\mathfrak{R}}_{S}(\mathcal{R})$ and $\Hat{\mathfrak{R}}_{S}(\mathcal{E})$ denote the em

Figures (4)

  • Figure 1: (a) Diagram of the standard learning to reject framework. (b) Diagram of the standard learning to defer framework. (c) Diagram of the learning to help for legacy model framework.
  • Figure 2: Testing Accuracy and Server Coverage Rate for Different Cost $c_e$. We test the training results for learning to help with fixed local model. Each sub-figure refers to binary classification on two different classes chosen from CIFAR-10.
  • Figure 3: Testing Accuracy Comparison on different Methods over Coverage Rate. We compare accuracy for the surrogate function with other two confidence-based methods as well as randomly reject model.
  • Figure :

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2: Calibration of Surrogate Loss, $L_{\text{S}}$
  • Theorem 3